<s>
More	O
generally	O
,	O
directional	O
statistics	O
deals	O
with	O
observations	O
on	O
compact	O
Riemannian	B-Architecture
manifolds	I-Architecture
including	O
the	O
Stiefel	O
manifold	O
.	O
</s>
<s>
The	O
matrix	O
von	O
Mises	O
–	O
Fisher	O
distribution	O
is	O
a	O
distribution	O
on	O
the	O
Stiefel	O
manifold	O
,	O
and	O
can	O
be	O
used	O
to	O
construct	O
probability	O
distributions	O
over	O
rotation	B-Algorithm
matrices	I-Algorithm
.	O
</s>
<s>
Since	O
a	O
versor	O
corresponds	O
to	O
a	O
rotation	B-Algorithm
matrix	I-Algorithm
,	O
the	O
Bingham	O
distribution	O
for	O
N	O
=	O
4	O
can	O
be	O
used	O
to	O
construct	O
probability	O
distributions	O
over	O
the	O
space	O
of	O
rotations	O
,	O
just	O
like	O
the	O
Matrix-von	O
Mises	O
–	O
Fisher	O
distribution	O
.	O
</s>
<s>
For	O
the	O
sample	O
the	O
circular	B-General_Concept
variance	I-General_Concept
is	O
defined	O
as	O
:	O
and	O
for	O
the	O
population	O
Both	O
will	O
have	O
values	O
between	O
0	O
and	O
1	O
.	O
</s>
<s>
Kuiper	B-General_Concept
's	I-General_Concept
test	I-General_Concept
for	O
possibly	O
multimodal	O
data	O
.	O
</s>
